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October | October | October | 1 - NUMBER THEORY SEMINAR: Number Theory Seminar: The limit multiplicities and von Neumann dimensions
Speaker: Jun Yang – Harvard 3:00 PM-4:00 PM November 1, 2023 1 Oxford Street, Cambridge, MA 02138 USA Given an arithmetic subgroup Γ in a semi-simple Lie group G, the multiplicity of an irreducible representation of G in L^2(Γ\G) is unknown in general. We observe the multiplicity of any discrete series representation pi of SL (2, R) in L^2 (Γ(n)\SL (2, R)) is close to the von Neumann dimension of pi over the group algebra of Γ(n). We extend this result to other Lie groups and bounded families of irreducible representations of them. By applying the trace formulas, we show the multiplicities are exactly the von Neumann dimensions if we take certain towers of descending lattices in some Lie groups. - SEMINARS: Informal Seminar on Dynamics, Geometry and Moduli Spaces: The 3D dimer model
Speaker: C. Wolfram – MIT 4:00 PM-5:00 PM November 1, 2023 Please see website for more details: www.math.harvard.edu/~ctm/sem. - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Topology of moduli spaces via combinatorics
Speaker: Madeline Brandt – Brown 4:15 PM-5:15 PM November 1, 2023
Deligne connects the weight-zero compactly supported cohomology of a moduli space to the combinatorics of its compactifications. This gives a method for using combinatorics to compute a piece of the cohomology of a moduli space. In this talk, we discuss this method for the cases of the moduli space of abelian varieties and the moduli space of n-marked hyperelliptic curves. =============================== For more info, see https://math.mit.edu/combin/ - OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: How to Build a Random Surface
Speaker: Scott Sheffield – MIT 4:30 PM-5:30 PM November 1, 2023 1 Oxford Street, Cambridge, MA 02138 USA The theory of “random surfaces” has emerged in recent decades as a significant field of mathematics, lying somehow at the interface between geometry, probability, combinatorics, analysis and mathematical physics. Just as “Brownian motion” is a special kind of random path, there is a similarly special kind of random surface. Random surfaces are often motivated by physics: statistical physics, string theory, quantum field theory, and so forth. They have also been independently studied by mathematicians working in random matrix theory and enumerative graph theory. But even without that motivation, one may be drawn to wonder what a “typical” two-dimensional manifold looks like, or how one can make sense of that question. I will give an overview of what this theory is about, including many computer simulations and illustrations. In particular, I will discuss the so-called Liouville quantum gravity surfaces, and explain how they are approximated by discrete random surfaces called random planar maps. =============================== https://people.math.harvard.edu/~gammage/ons/
| 2 - CMSA EVENT: CMSA Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar: Landscape of quantum phases in quantum materials
Speaker: Liujun Zou – Perimeter 4:30 PM-6:00 PM November 2, 2023 20 Garden Street, Cambridge, MA 02138 A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose, one should be able to not only describe the quantum phases using some effective field theories, but also capture the important microscopic information of the material via mathematical formulation. In this talk, I will present a framework to classify quantum phases in quantum materials, where the microscopic information of a material is encoded in its quantum anomaly. I will talk about the application of this framework to classify various exotic quantum phases of matter in different lattice systems. Using our framework, we have obtained many results unexpected from the previous literature. Zoom: https://harvard.zoom.us/j/977347126 Password: cmsa
| 3 - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Tiling, Sodoku, Domino, and Decidability
Speaker: Rachel Greenfeld – IAS 3:00 PM-4:00 PM November 3, 2023
Translational tiling is a covering of a space (such as Euclidean space) using translated copies of one building block, called a “translational tile”, without any positive measure overlaps. Can we determine whether a given set is a translational tile? Does any translational tile admit a periodic tiling? A well known argument shows that these two questions are closely related. In the talk, we will discuss this relation and present some new developments, joint with Terence Tao, establishing answers to both questions. =============================== For more info, see https://math.mit.edu/combin/
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5 | 6 - CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: Deformations of Landau-Ginzburg models and their fibers
Speaker: Andrew Harder – Lehigh 10:30 AM-11:30 AM November 6, 2023 20 Garden Street, Cambridge, MA 02138 In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y,w), and in particular, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces. - CMSA EVENT: CMSA Colloquium: Impossibility results in classical dynamical systems.
Speaker: Matthew Foreman – University of California Irvine 4:30 PM-5:30 PM November 6, 2023 20 Garden Street, Cambridge, MA 02138 In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960’s, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems. These questions laid the groundwork for enormous amounts of work, but the fundamental questions remain open. This talk shows that they are impossible to answer in a rigorous sense. The talk will discuss various kinds of impossibility results and describe how they apply to von Neumann’s program and Smale’s program.
| 7 - CMSA EVENT: CMSA General Relativity Seminar: Fluid stabilization in slowly expanding cosmological spacetimes
Speaker: David Fajman – University of Vienna 11:00 AM-12:00 PM November 7, 2023 20 Garden Street, Cambridge, MA 02138
Relativistic fluids are known to form shocks during their evolution from near-homogeneous initial data. In expanding spacetimes, shock formation is suppressed, if the expansion is sufficiently strong. We refer to this effect as fluid stabilization. The occurrence of this phenomenon depends on features of the fluid and has implications for our understanding of structure formation and cosmological evolution. While the effect is well studied in the regime of accelerated expansion, in recent years it has been shown that fluid stabilization occurs as well in spacetimes with slower expansion rates. In this talk we present different recent results on fluid stabilization in slowly expanding spacetimes and aspects of the methods involved in the respective proofs.
Zoom: https://harvard.zoom.us/j/7855806609 Password: cmsa - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: CANCELLED – Harvard-MIT Algebraic Geometry Seminar: Angle ranks of Abelian varieties
Speaker: David Zureick-Brown – Amherst College 3:00 PM-4:00 PM November 7, 2023 1 Oxford Street, Cambridge, MA 02138 USA Due to unforeseen circumstances, his event has been CANCELLED. I will discuss an elementary notion — the angle rank of a polynomial — and an application to the Tate conjecture for Abelian varieties over finite fields. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
| 8 - CMSA EVENT: CMSA New Technologies in Mathematics Seminar: Peano: Learning Formal Mathematical Reasoning Without Human Data
Speaker: Gabriel Poesia – Stanford Dept. of Computer Science 2:00 PM-3:00 PM November 8, 2023 20 Garden Street, Cambridge, MA 02138 Recent progress in game-playing AI has prompted the question: how might we create AIs that master the game of mathematics? Modern interactive theorem provers like Lean or Coq provide most of this analogy by defining states, actions and rewards after given a theorem statement. However, they expose an infinite action space, which makes learning from scratch challenging. I’ll introduce Peano, a minimal theorem-proving environment based on dependent type theory that exposes a finite action space. This feature allows an agent to start tabula rasa in a new domain and learn to solve problems. I’ll first describe a case study on learning to solve simple algebra problems from five sections of the Khan Academy platform. Reinforcement learning alone fails to progress towards the hardest problems, as solutions in terms of the base action space grow longer with increasing problem complexity. Having the agent induce its own tactics — higher-level actions that compress solutions found so far — allows it to make steady progress, solving all problems and guiding it towards human-like solutions. Furthermore, these tactics induce an order to the problems, despite being seen at random during training. The recovered order has significant agreement with the expert-designed Khan Academy curriculum, and second-generation agents trained on the recovered curriculum learn significantly faster. Finally, I’ll describe ongoing work on solving the Natural Number Game — a popular introduction to theorem proving in Lean for mathematicians. The finite action space allows us to train agents by borrowing ideas from curiosity-driven exploration in Reinforcement Learning. Notably, simply trying to find “interesting” consequences of the hypotheses of a theorem — as measured by the surprisal of a language model — often leads to proving the theorem itself. https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09 Password: cmsa - NUMBER THEORY SEMINAR: Number Theory Seminar: ℓ-adic images of Galois for elliptic curves over ℚ
Speaker: David Zureick-Brown – Amherst College 3:00 PM-4:00 PM November 8, 2023 1 Oxford Street, Cambridge, MA 02138 USA I will discuss recent joint work with Jeremy Rouse and Drew Sutherland on Mazur’s “Program B” — the classification of the possible “images of Galois” associated to an elliptic curve (equivalently, classification of all rational points on certain modular curves Xʜ. The main result is a provisional classification of the possible images of ℓ-adic Galois representations associated to elliptic curves over ℚ and is provably complete barring the existence of unexpected rational points on modular curves associated to the normalizers of non-split Cartan subgroups and two additional genus 9 modular curves of level 49. I will also discuss the framework and various applications (for example: a very fast algorithm to rigorously compute the ℓ-adic image of Galois of an elliptic curve over ℚ, and then highlight several new ideas from the joint work, including techniques for computing models of modular curves and novel arguments to determine their rational points, a computational approach that works directly with moduli and bypasses defining equations, and (with John Voight) a generalization of Kolyvagin’s theorem to the modular curves we study. - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Cross-Ratio Degrees
Speaker: Matt Larson – Stanford 4:15 PM-5:15 PM November 8, 2023
Given n-3 subsets of {1, …, n} of size 4, the cross-ratio degree counts the number of ways to place n marked points on the Riemann sphere such that the n-3 cross-ratios are prescribed generic complex numbers. If more than k-3 of the sets involve just k of the points, then those k points are overdetermined and the cross-ratio degree vanishes. We show that this is the only reason why a cross-ratio degree can vanish: if no subset of the points is overdetermined, then the cross-ratio degree is positive. This gives a new proof of Laman’s theorem characterizing graphs whose generic embedding in the plane is rigid. Joint with Joshua Brakensiek, Christopher Eur, and Shiyue Li. =============================== For more info, see https://math.mit.edu/combin/
| 9 - CMSA EVENT: CMSA Active Matter Seminar: Nuclear chromodynamics: non-equilibrium phase transition in the nucleus of a living cell
Speaker: Alexander Grosberg – NYU 1:00 PM-2:00 PM November 9, 2023 20 Garden Street, Cambridge, MA 02138 Nucleus of a living cell houses a cell genome – a polymer called chromatin, which is a functional form of DNA. It is very long, e.g., 2 meters long for every human cell. Nucleus is also an arena of incessant energy-driven activity. Experiments show that chromatin undergoes large scale motions sustained over long times of order seconds. In the talk, after reviewing the phenomenology, I will show how these flows may arise due to a phase transition in which chromatin-driving motors, such as RNA polymerase, form a polar (“ferromagnetic”) order controlled by hydrodynamic interactions. The talk is based on the joint work with I.Eshghi and A.Zidovska. Lunch served at 12:30.
This seminar will be held in person and on Zoom. https://harvard.zoom.us/j/96657833341 Password: cmsa - THURSDAY SEMINAR SEMINAR: Thursday Seminar: Invertible field theories and stable homotopy theory
Speaker: Natalia Pacheco-Tallaj – 3:30 PM-5:30 PM November 9, 2023 1 Oxford Street, Cambridge, MA 02138 USA Thursday Seminar given by Natalia Pacheco-Tallaj on “Invertible field theories and stable homotopy theory.”
| 10 - GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR: Gauge Theory and Topology Seminar: Complex Chern-Simons invariants of 3-manifolds via abelianization
Speaker: Dan Freed – Harvard 3:30 PM-4:30 PM November 10, 2023 1 Oxford Street, Cambridge, MA 02138 USA
A hyperbolic 3-manifold M carries a flat PSL(2;C)-connection whose Chern-Simons invariant has been much studied since the early 1980’s. For example, its real part is the volume of M. Explicit formulas in terms of a triangulation involve the dilogarithm. In joint work with Andy Neitzke we use 3-dimensional spectral networks to abelianize the computation of complex Chern-Simons invariants. The locality of the Chern-Simons invariant, expressed in the language of topological field theory, plays an important role. The dilogarithm arises from a novel construction involving Chern-Simons invariants of flat C*-connections over a 2-torus.
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12 | 13 - CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa invariants
Speaker: Sheldon Katz – UIUC 10:30 AM-11:30 AM November 13, 2023 20 Garden Street, Cambridge, MA 02138 A determinantal octic double solid is the double cover X of P^3 branched along the degree 8 determinant of a symmetric matrix of homogeneous forms on P^3. These X are nodal CY threefolds which do not admit a projective small resolution. B-model techniques can be applied to compute GV invariants up to g \le 32. This raises the question: what is the geometric meaning of these invariants? Evidence suggests that these enumerative invariants are associated with moduli stacks of coherent sheaves of modules over a sheaf B of noncommutative algebras on X constructed by Kuznetsov. One of these moduli stacks is a stacky small resolution X’ of X itself. This leads to another geometric interpretation of the invariants as being associated with moduli of sheaves on X’ twisted by a Brauer class. Geometric computations based on these working definitions always agree with the B-model computations. This talk is based on joint work with Albrecht Klemm, Thorsten Schimannek, and Eric Sharpe - SPECIAL SEMINAR SEMINAR: Special Seminar: Moments of L-functions via the homology of braid groups
Speaker: Craig Westerland – University of Minnesota 3:00 PM-4:00 PM November 13, 2023 1 Oxford Street, Cambridge, MA 02138 USA In 2005, Conrey, Farmer, Keating, Rubinstein, and Snaith posed a conjecture on the asymptotics of moments of quadratic L-functions. While this conjecture originates as a question about number fields, it has a more geometric version when posed over function fields in positive characteristic. I’ll talk about how one can reinterpret the central object in this conjecture in terms of the action of the Galois group of a finite field on the cohomology of braid groups with certain coefficients coming from the braid group’s interpretation as the hyperelliptic mapping class group. We will see the “arithmetic factor” in this conjecture appear in the part of this cohomology that is accessible through tools of homological stability. This is joint work with Jonas Bergström, Adrian Diaconu, and Dan Petersen. - CMSA EVENT: CMSA Colloquium: Koszul duality in QFT
Speaker: Brian Williams – Boston University 4:30 PM-5:30 PM November 13, 2023 20 Garden Street, Cambridge, MA 02138 We will describe appearances of the algebraic phenomena of Koszul duality in the context of boundary conditions and defects in quantum field theory. Primarily motivated by topological string theory, this point of view was pioneered by Costello and Li in their proposal for a twisted version of the AdS/CFT correspondence. Since then, many important examples of (twisted) holographic dualities in string and M-theory have been studied in work of Costello, Gaiotto, Paquette and many others. I will survey some of these examples and some current work with Raghavendran and Saberi which uses this formalism to predict exceptional symmetries present in M-theory.
| 14 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: Superadditivity of anticanonical Iitaka dimension in positive characteristic
Speaker: Iacopo Brivio – CMSA 3:00 PM-4:00 PM November 14, 2023 1 Oxford Street, Cambridge, MA 02138 USA Given a fibration $f\colon X\to Y$ of smooth complex projective with general fiber $F$, the celebrated Iitaka conjecture predicts the inequality $\kappa(K_X)\geq \kappa(K_F)+\kappa(K_Y)$. Recently Chang showed that, under some natural conditions, the inequality $\kappa(-K_X)\leq \kappa(-K_F)+\kappa(-K_Y)$ holds. In this talk I will show that, despite the failure in positive characteristic of both the Iitaka conjecture and Chang’s theorem, it is possible to recover the latter for “tame” positive characteristic fibrations. This is based on joint work with M. Benozzo and C.-K. Chang. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar - OTHER MATHEMATICS DEPARTMENT EVENTS: Physical and Mathematical Sciences Virtual Open House
3:00 PM-5:00 PM November 14, 2023 Agenda: 3:00-4:00 PM EST (GMT -4:00): PhD Admissions Panel 4:00-5:00 PM EST (GMT -4:00): Breakout Session Q&As with PhD Programs We hope you will join us to: –Learn about physical and mathematical sciences PhD programs at Harvard –Connect with current faculty, staff, and students –Learn about how to put together a strong application At the end of the Admissions Panel, you will receive Zoom links for the individual PhD program breakout sessions Registration link https://harvard.zoom.us/webinar/register/WN_CEaHSF-pTA6z-Xix62P5tw
| 15 - CMSA EVENT: CMSA New Technologies in Mathematics Seminar: Peano: On the Power of Forward pass through Transformer Architectures
Speaker: Abhishek Panigrahi – Princeton Dept. of Computer Science 2:00 PM-3:00 PM November 15, 2023 20 Garden Street, Cambridge, MA 02138 Highly trained transformers are capable of interesting computations as they infer for an input. The exact mechanism that these models use during forward passes is an interesting area of study. This talk studies two interesting phenomena.In the first half, we explore how and why pre-trained language models, specifically BERT of moderate sizes, can effectively learn linguistic structures like parse trees during pre-training. Specifically, using synthetic data through PCFGs, we show how moderate-sized transformers can perform forward-backward parsing, also known as the inside-outside algorithm, during inference. We further understand the role of the pre-training loss for the model to learn to parse during pre-training. In the second half, we consider in-context learning of large language models, where they learn to reason on the fly. An ongoing hypothesis is that transformers simulate gradient descent at inference to perform in-context learning. We propose the Transformer in Transformer (TinT) framework, which creates explicit transformer architectures that can simulate and fine-tune a small pre-trained transformer model during inference. E.g. a 1.3B parameter TINT model can simulate and fine-tune a 125 million parameter model in a single forward pass. This framework suggests that large transformers might execute intricate sub-routines during inference, and provides insights for enhancing their capabilities through intelligent design considerations. https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09 Password: cmsa - NUMBER THEORY SEMINAR: Number Theory Seminar: Semisimplicity and CM lifts
Speaker: Ananth Shankar – Northwestern University 3:00 PM-4:00 PM November 15, 2023 1 Oxford Street, Cambridge, MA 02138 USA Consider the setting of a smooth variety $S$ over $\mathbb{F}_q$, and an $\ell$-adic local on $S$ which has finite determinant and is geometrically irreducible. Work of Lafforgue proves that such a local system must be pure, and it is conjectured that the action of Frobenius at closed points is semisimple. I will sketch a proof of this conjecture in the setting of mod $p$ Shimura varieties, and will deduce applications to the existence of CM lifts of certain mod p points. If time permits, I will also address the question of integral canonical models of Shimura varieties. This is joint work with Ben Bakker and Jacob Tsimerman. - SEMINARS: Informal Seminar on Dynamics, Geometry and Moduli Spaces: Multipliers of rational maps
Speaker: Laura DeMarco – Harvard 4:00 PM-5:00 PM November 15, 2023 Please see website for more details: www.math.harvard.edu/~ctm/sem. - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Totally Nonnegative Springer Fibres are contractible
Speaker: Haunchen Bao – National University of Singapore 4:15 PM-5:15 PM November 15, 2023
Discrete Morse theory, developed by Forman, is an efficient tool to determine the homotopy type of a regular CW complex. The theory has been reformulated by Chari in purely combinatorial terms of acyclic matchings on the face poset. In this talk, I will discuss explicit constructions of such acyclic matchings on Bruhat intervals using reflection orders. As an application, we show the totally nonnegative Springer fibres are contractible, verifying a conjecture of Lusztig. This is based on work in progress with Xuhua He. =============================== For more info, see https://math.mit.edu/combin/ - OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: Knots, tangles, braids, and rational numbers
Speaker: Joshua Wang – MIT 4:30 PM-5:30 PM November 15, 2023 1 Oxford Street, Cambridge, MA 02138 USA
The subject of knot theory concerns the phenomena of “knotting”, “tangling”, and “braiding”, investigated from a mathematical point of view. I’ll discuss a family of tangles called rational tangles and the related concepts of 2-bridge knots and plat closures of 4-braids. Rational tangles are named after John Conway’s remarkable classification of them: they admit a natural one-to-one correspondence with the rational numbers (and infinity). =============================== https://people.math.harvard.edu/~gammage/ons/
| 16 | 17 - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Random Reconstruction in Two Dimensions
Speaker: Bhargav Narayanan – Rutgers 3:00 PM-4:00 PM November 17, 2023
Suppose that we only see small “k x k snapshots” of a random two-dimensional “n x n picture”: can we piece the original picture back together? Motivated by the one-dimensional problem of shotgun sequencing DNA, Mossel and Ross raised several interesting questions (like the one aforementioned) about reconstructing random structures from “small snapshots” in two (and higher) dimensions. In this talk, I will sketch how we can now answer some of these two-dimensional reconstruction questions: in particular, it turns out that the answer to the problem mentioned above exhibits somewhat surprising “two-point concentration,” and getting to this answer involves a combination of entropic methods and tools from percolation. =============================== For more info, see https://math.mit.edu/combin/ - GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR: Gauge Theory and Topology Seminar: Rank three instantons, representations and sutures
Speaker: Ali Daemi – Washington University in Saint Louis 3:30 PM-4:30 PM November 17, 2023 1 Oxford Street, Cambridge, MA 02138 USA
ng-Mills gauge theory with gauge group SU(2) has played a significant role in the study of the topology of 3- and 4-manifolds. It is natural to ask whether we obtain more topological information by working with other choices of gauge groups such as SU(n) for higher values of n. Mariño and Moore formulated a conjecture essentially stating that there is no new information in Donaldson invariants of smooth 4-manifolds defined using SU(n) Yang-Mills gauge theory. Despite this “negative” prediction, one might still hope that there is still novel information about 3-manifolds in higher rank gauge theory. In this talk, I will discuss a result about the topology of 3-manifolds obtained using gauge theory with respect to the Lie group SU(3): for any knot K in the 3-dimensionl sphere (or more generally an integer homology sphere) there is a non-abelian representation of the knot group of K into SU(3) such that the homotopy class of the meridian of K is mapped to a matrix with eigenvalues 1, w, w^2 with w being a primitive third root of unity. As a byproduct of the proof, we obtain a structure theorem for SU(3) Donaldson invariants of 4-manifolds, analogous to Kronheimer and Mrowka’s structure theorem for SU(2) Donaldson invariants. This can be regarded as a piece of evidence supporting Mariño and Moore’s conjecture. This talk is based on a recent joint work with Nobuo Iida and Chris Scaduto.
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19 | 20 - CMSA EVENT: CMSA/Tsinghua Math-Science Literature Lecture: Scott Kominers
Speaker: Scott Kominers – 9:00 AM-10:30 PM November 20, 2023 For more information and to register online, please see: https://cmsa.fas.harvard.edu/event/mathscilit2023/ - CMSA EVENT: CMSA Colloquium: The analytical challenges of connectomics
Speaker: Jeff W. Lichtman – Harvard University (Jeremy R. Knowles Professor of Molecular and Cellular Biology) 4:30 PM-5:30 PM November 20, 2023 20 Garden Street, Cambridge, MA 02138 Recent progress in generating synapse-level maps of brains, a field known as connectomics, brings both opportunities and challenges. The upside is that the biophysical instantiation of memories, behaviors, and knowledge will soon be before us. The downside is that no one knows exactly how to make sense of this data. I will show what connectomics data sets are and attempt to explain why it is so difficult to unravel their meaning.
| 21 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: The Noether-Lefschetz loci formed by determinantal surfaces in projective 3-space.
Speaker: César Lozano Huerta – Universidad Nacional Autónoma de México 3:00 PM-4:00 PM November 21, 2023 1 Oxford Street, Cambridge, MA 02138 USA Solomon Lefschetz showed that the Picard group of a general surface in P3 of degree greater than three is ZZ. That is, the vast majority of surfaces in P3 have the smallest possible Picard group. The set of surfaces of degree greater than 3 on which this theorem fails is called the Noether-Lefschetz locus. This locus has infinite components and their dimensions are somehow mysterious. In this talk, I will calculate the dimension of infinite Noether-Lefschetz components that are simple in a sense, but still give us an idea of the complexity of the entire Noether-Lefschetz locus. This is joint work with Montserrat Vite and Manuel Leal. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
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26 | 27 - CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: a p-adic Laplacian on the Tate curve
Speaker: An Huang – Brandeis University 10:30 AM-11:30 AM November 27, 2023 20 Garden Street, Cambridge, MA 02138 We shall first explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis. We then propose a genus one p-adic string worldsheet action. The key is the definition of a p-adic Laplacian operator on the Tate curve. We show that the genus one p-adic Green’s function exists, is unique under some obvious constraints, is locally constant off diagonal, and has a reflection symmetry. It can also be numerically computed exactly off the diagonal, thanks to some simplifications due to the p-adic setup. Numerics suggest that at least in some special cases, the asymptotic behavior of the Green’s function near the diagonal is a direct p-adic counterpart of the familiar Archimedean case, although the p-adic Laplacian is not a local operator. Joint work in progress with Rebecca Rohrlich. - CMSA EVENT: CMSA Colloquium: What do topological dynamics, combinatorics, and model theory have in common?
Speaker: Dana Bartosova – University of Florida 4:30 PM-5:30 PM November 27, 2023 20 Garden Street, Cambridge, MA 02138 A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris, Pestov, and Todocevic. Since then, their work has been generalized and applied in many directions. It also struck a fresh wave of interest in finite Ramsey theory. Many classes of finite structures are shown to have the Ramsey property by encoding their problem in a known Ramsey class and translating a solution back. This is often a case-by-case approach and naturally there is a great need for abstracting the process. There has been much success on this front, however, none of the tools captures every situation. We will discuss one such encoding via a model-theoretic notion of semi-retraction introduced by Lynn Scow in 2012. In a joint work, we showed that a semi-retraction transfers the Ramsey property from one class of structures to another under quite general conditions. We compare semi-retractions to a category-theoretical notion of pre-adjunction revived by Mašulović in 2016. If time permits, I will mention a transfer theorem of the Ramsey property from a class of finite structures to their uncountable ultraproducts, which is an AIMSQuaRE project with Džamonja, Patel, and Scow.
| 28 - CMSA EVENT: CMSA General Relativity Seminar: Remarkable symmetries of rotating black holes
Speaker: David Kubiznak – Charles University 11:00 AM-12:00 PM November 28, 2023 20 Garden Street, Cambridge, MA 02138 It is well known that the Kerr geometry admits a non-trivial Killing tensor and its `square root’ known as the Killing-Yano tensor. These two objects stand behind Carter’s constant of geodesic motion as well as allow for separability of test field equations in this background. The situation is even more remarkable in higher dimensions, where a single object — the principal Killing-Yano tensor — generates a tower of explicit and hidden symmetries responsible for integrability of geodesics and separability of test fields around higher-dimensional rotating black holes. Interestingly, similar yet different structure is already present for the slowly rotating black holes described by the `magic square’ version of the Lense-Thirring solution, giving rise to a geometrically preferred spacetime that can be cast in the Painleve-Gullstrand form and admits a tower of exact rank-2 and higher rank Killing tensors whose number rapidly grows with the number of spacetime dimensions.
Zoom: https://harvard.zoom.us/j/7855806609 Password: cmsa - CMSA EVENT: Special Probability Seminar: A random matrix model towards the quantum chaos transition conjecture
Speaker: Jun Yin – UCLA 12:00 PM-1:00 PM November 28, 2023 The Quantum Chaos Conjecture has long fascinated researchers, postulating a critical spectrum phase transition that separates integrable systems from chaotic systems in quantum mechanics. In the real of integrable systems, eigenvectors remain localized, and local eigenvalue statistics follow the Poisson distribution. Conversely, chaotic systems exhibit delocalized eigenvectors, with local eigenvalue statistics mirroring the Sine kernel distribution, akin to the standard random matrix ensembles GOE/GUE. This talk delves into the heart of the Quantum Chaos Conjecture, presenting a novel approach through the lens of random matrix models. By utilizing these models, we aim to provide a clear and intuitive demonstration of the same phenomenon, shedding light on the intricacies of this long-standing conjecture. - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: Properties of log canonical singularities in positive characteristic
Speaker: Emelie Arvidsson – University of Utah 3:00 PM-4:00 PM November 28, 2023 1 Oxford Street, Cambridge, MA 02138 USA We will investigate if some well known properties of log canonical singularities over the complex numbers still hold true over perfect fields of positive characteristic and over excellent rings with perfect residue fields. We will discuss both pathological behavior in characteristic p as well as some positive results for threefolds. We will see that the pathological behavior of these singularities in positive characteristic is closely linked to the failure of certain vanishing theorems in positive characteristic. Additionally, we will explore how these questions are related to the moduli theory of varieties of general type. This is based on joint work with F. Bernasconi and Zs. Patakfalvi, as well as joint work with Q. Posva. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
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